When someone is injured as a pedestrian, they become a claimant on the at fault party's claim. Given that the person who hit you was identified, you will be claiming under their Bodily Injury section which is part of their Third Party Liability coverage.

Your first source of coverage is your own AB section on your policy. If you don't have that or you go past your limit of coverage you claim under the BI of the other party.

Is there any recourse for the injured pedestrian if they have no insurance of their own/in their household and the "at fault party" is also not insured (as in the scenario described above) or not identified (hit and run)?